From German Patent Application No. DE 101 14 470, a tracking and vehicle speed control device for motor vehicles is known by which the course of the traffic lane and the position of a vehicle relative to the traffic lane it is driving in are ascertained with the aid of video-based lane detection. Signals derived from the course of the traffic lane and the position of the vehicle are transmitted to a warning device, which outputs an acoustic warning signal, for example, so as to alert the driver of an imminent undesired lane change. Such a video-based lane detection often yields unsatisfactory results in detecting the road course, especially in the case of roads with sharp bends. Much too often this is accompanied by false warnings of the warning device, which alert the driver of a lane change allegedly taking place. As soon as the driver becomes aware of these unfounded error alerts, the warnings tend to be disregard and overridden. The acceptance of this assistance system, which was actually meant to make driving less complicated for the driver, ultimately suffers. The cause of frequent false alerts may be roads that are not designed for such an assistance system and thus overtax it. Frequent errors in the lane detection must be expected, for instance, in the case of roads that have a radius of curvature of less than 100 m. This situation is often encountered on inner-city streets and also on entrance and exit ramps of expressways and highways. Furthermore, especially in inner cities, lane demarcations are disregarded by drivers and sometimes even intentionally ignored, for example, when trying to keep the greatest possible lateral distance from obstacles appearing along the edge of the road or with respect to other persons driving in too unsafe a manner, such as bicyclists. In such situations the emitting of a warning signal alerting the driver to a lane change tends to be undesired since it interrupts the driver and distracts him from the traffic situation.